In the early hours of Saturday 15 October 2011, vandals threw a brick through the door of the 72-year-old’s home in Hambleton Place, Thirsk, and left a petrol can outside the property.
In the second incident, just before midnight on Monday 17 October, a boulder was thrown through her window and a petrol can left inside the property.
Police are carrying out door-to-door enquiries in the local area and are appealing for anyone who knows anything about the incidents to come forward.
Inspector David Murray of Thirsk Safer Neighbourhood Team, said:
The two incidents are very disturbing and we are determined to find out who is behind them.
The victim, who is in her 70s, is naturally very upset by these events and is struggling to understand why anyone would want to target her in this way.
I am appealing to members of the public to help us solve this distressing crime.
Anyone who saw anything suspicious on either evening, can identify those responsible or has any information that could assist the investigation is urged to come forward to the police without delay.
If you do not wish to give your name, you can call the independent charity Crimestoppers and give information anonymously.
Anyone who can help is asked to call North Yorkshire Police on 0845 60 60 247, quoting reference 12110176594, or call Crimestoppers anonymously on 0800 555 111.
Police will be carrying out reassurance patrols this evening and distributing leaflets in the area.